Low-capacitance Josephson junctions, where Cooper pairs tunnel coherently while Coulomb blockade effects allow the control of the total charge, provide physical realizations of quantum bits (qubits), with logical states differing by one Cooper-pair charge on an island. The single- and two-bit operations required for quantum computation can be performed by applying a sequence of gate voltages (Shnirman et al., 1997). The phase coherence time is sufficiently long to allow a series of operations. A new design (Makhlin et al., 1999), close to ideal, where the Josephson junctions are replaced by controllable SQUIDs relaxes the requirements on the time control and system parameters substantially, and the two-bit coupling can be switched exactly between zero and a non-zero value for arbitrary pairs.